**4. Formation of ice deposit**

After caves were formed, ice may be generated gradually in a suitable climate. For basaltic cave (or lava tube), there may be a clear time boundary between cave formation and ice formation, because lava tubes are steady in water circulation. For limestone cave, there is no such clear time boundary due to limestone instability in wet environments during the geological period.

#### **4.1 Qualitative analysis of cave cooling by air convection**

There are variable hypotheses about the preservation mechanism of ice body in Ningwu ice cave. Chen [21] proposed that there is a "cold source" below Ningwu ice cave, which generates the negative geothermal anomaly and then preserves the ice

**91**

can be kept.

air natural convection [27].

*4.2.1 Basic ideas of simulation*

caves.

*A Review of Chinese Ice Caves*

1.0–3.0°C (100 m)<sup>−</sup><sup>1</sup>

*DOI: http://dx.doi.org/10.5772/intechopen.89178*

ensure the existence of the ice deposit.

body. Meng et al. [20] ascribed the existence of ice deposit to the combined effect of multiple factors, i.e., geographical location, the "icehouse effect," the "chimney effect," and the "thermal effect" produced by the ice deposit and the "millennial volcano." Unfortunately, they did not supply more details on these factors. Gao et al. [19] considered two aspects, terrain and climate, and proposed that far more cold air than warm air entered the region, and thus the ice cave stayed cold over a year. The subsurface temperature usually rises with depth at a geothermal gradient of

ground. Furtherly, even if a cold region had somehow formed, it would be warmed up by the geothermal flux through the geological period, because the host rock successively transfer heat energy to the "cold source." At another point, it is a temperate climate outside of the cave. It is difficult to maintain ice deposit in a warm climate without an efficient cooling mechanism. Therefore, we proposed that there must be a sustainable and efficient mechanism to remove the heat from underneath and

There is an annual cyclic variation on the air temperature outside Ningwu ice cave: it is warmer than the inside temperature in spring, summer, and autumn, but colder in winter. Because Ningwu ice cave has only a single opening at the top of the cave, cold air of the ice cave could be relatively heavy in spring, summer, and autumn and sinks into the bottom of the cave. Thus, it will not generate air natural thermal convection. In these three seasons, heat energy is transferred by conduction from outside down to the ice cave and from wall rock because of the terrestrial heat flux. Thermal conductivities are low for either wall rock (limestone) or air, and thus the conductive heat transfer efficiency is low. Consequently, the energy conducted to the inside of ice cave in these three seasons is quite limited. However, in winter, it is colder than the inside of the cave, and thus the air outside of ice cave could be heavier than the inside. Gravitational instability is generated, and air thermal convection could occur. The outside cold air promptly flows into the cave to cool it down, and it removes the heat energy out of the cave, which is conducted into the cave from the host rock and through the opening in spring, summer, and autumn. Convective heat transfer is much more efficient than conduction; therefore, the heat energy convected out of the cave in winter is enough to balance the heat conducted into the cave year-round. The annual heat budget of income and output is balanced, so the cave would be in a cyclic state with very small temperature fluctuations, and the average temperature is always lower than 0°C; thus ice deposits in the ice cave

Studies in Zibaishan and Wudalianchi ice caves were still at a relatively low level by far. We proposed that similar air convection cooling could occur in these two ice

Accurately, ice forming and melting in caves include at least three physical processes: water flow in porous media (limestone), natural convection of low viscous material (air), and water-ice phase change. The numerical simulation of each process involves complex mathematical method, especially the second physical process. Based on some assumptions, an equivalent method was used to deal with

Two heat transfer processes must be considered to interpret the existence of ice deposits in Ningwu ice cave, i.e., thermal conduction and convection. The water-ice

**4.2 Quantitative calculation of ice forming and melting**

[26], which cannot support a permanent "cold source" under-

#### *A Review of Chinese Ice Caves DOI: http://dx.doi.org/10.5772/intechopen.89178*

*Earth Crust*

**Figure 4.**

**Figure 5.**

*stress (modified from [25]).*

**90**

depth would be easier ruptured than normal ones (**Figure 5c**). Elliptical lava tubes

*Maximum principal stresses at the top (dashed line) and bottom (solid line) side of a normal (a), a bigger (b), a deeper (c), and an elliptical (d) lava tube, respectively. The normal lava tube with 10 m diameter and 5 m buried depth. The bigger lava tube with 16 m diameter and 5 m buried depth. The deeper lava tube with 10 m diameter and 8 m buried depth. The elliptical lave tube with 12 m long axis, 8 m short axis, and 5 m buried* 

*Principle stress distributions around the lava tube. (a) Maximum principal stress and (b) minimum principal* 

After caves were formed, ice may be generated gradually in a suitable climate. For basaltic cave (or lava tube), there may be a clear time boundary between cave formation and ice formation, because lava tubes are steady in water circulation. For limestone cave, there is no such clear time boundary due to limestone instability in

There are variable hypotheses about the preservation mechanism of ice body in Ningwu ice cave. Chen [21] proposed that there is a "cold source" below Ningwu ice cave, which generates the negative geothermal anomaly and then preserves the ice

would be more stable than normal lava tubes (**Figure 5d**).

**4.1 Qualitative analysis of cave cooling by air convection**

wet environments during the geological period.

**4. Formation of ice deposit**

*depth (modified from [25]).*

body. Meng et al. [20] ascribed the existence of ice deposit to the combined effect of multiple factors, i.e., geographical location, the "icehouse effect," the "chimney effect," and the "thermal effect" produced by the ice deposit and the "millennial volcano." Unfortunately, they did not supply more details on these factors. Gao et al. [19] considered two aspects, terrain and climate, and proposed that far more cold air than warm air entered the region, and thus the ice cave stayed cold over a year. The subsurface temperature usually rises with depth at a geothermal gradient of 1.0–3.0°C (100 m)<sup>−</sup><sup>1</sup> [26], which cannot support a permanent "cold source" underground. Furtherly, even if a cold region had somehow formed, it would be warmed up by the geothermal flux through the geological period, because the host rock successively transfer heat energy to the "cold source." At another point, it is a temperate climate outside of the cave. It is difficult to maintain ice deposit in a warm climate without an efficient cooling mechanism. Therefore, we proposed that there must be a sustainable and efficient mechanism to remove the heat from underneath and ensure the existence of the ice deposit.

There is an annual cyclic variation on the air temperature outside Ningwu ice cave: it is warmer than the inside temperature in spring, summer, and autumn, but colder in winter. Because Ningwu ice cave has only a single opening at the top of the cave, cold air of the ice cave could be relatively heavy in spring, summer, and autumn and sinks into the bottom of the cave. Thus, it will not generate air natural thermal convection. In these three seasons, heat energy is transferred by conduction from outside down to the ice cave and from wall rock because of the terrestrial heat flux. Thermal conductivities are low for either wall rock (limestone) or air, and thus the conductive heat transfer efficiency is low. Consequently, the energy conducted to the inside of ice cave in these three seasons is quite limited. However, in winter, it is colder than the inside of the cave, and thus the air outside of ice cave could be heavier than the inside. Gravitational instability is generated, and air thermal convection could occur. The outside cold air promptly flows into the cave to cool it down, and it removes the heat energy out of the cave, which is conducted into the cave from the host rock and through the opening in spring, summer, and autumn. Convective heat transfer is much more efficient than conduction; therefore, the heat energy convected out of the cave in winter is enough to balance the heat conducted into the cave year-round. The annual heat budget of income and output is balanced, so the cave would be in a cyclic state with very small temperature fluctuations, and the average temperature is always lower than 0°C; thus ice deposits in the ice cave can be kept.

Studies in Zibaishan and Wudalianchi ice caves were still at a relatively low level by far. We proposed that similar air convection cooling could occur in these two ice caves.
